The method of quasi-homogeneous functions and the Pock problem

The problem of high frequency diffraction by a smooth convex body is investigated in the vicinity of the point where a limit ray is tangent the boundary of the body. It is shown that the problem may be formulated as a scattering one for Schrodinger equation. By using the technique of a'priory estimations, and the formal solutions of Schrodinger equation in form of quasi-homogeneous functions, the theorems of existence, uniqueness and smoothness of the problem's solution are proved.